The entire genome in each cell contains all of the genes for every type of cell in your body. In different types of cells and in different states certain genes are upregulated and downregulated. Essentially the process for turning a specific gene into the protein it codes for can be turned on or off. That is what is meant by an active vs inactive gene.

Note: the activity of a neuron and the activity of a specific gene (eg rac1) are two completely different kinds of activity. The first is electrochemical activity and the second is production activity. Where changes in production can change the physical number of receptors available for the electrochemcial process.